The Economist Numbers Guide: The Essentials of Business Numeracy

257 Pages·2007·2.8 MB·English

Numbers Guide 5th edn rev3/31 10/19/06 2:49 PM Page i
NUMBERS GUIDE
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OTHER ECONOMIST BOOKS
Guide to Analysing Companies
Guide to Business Modelling
Guide to Economic Indicators
Guide to the European Union
Guide to Financial Markets
Guide to Management Ideas
Style Guide
Business Ethics
China’s Stockmarket
Economics
E-Commerce
E-Trends
Globalisation
Measuring Business Performance
Successful Innovation
Successful Mergers
Wall Street
Dictionary of Business
Dictionary of Economics
International Dictionary of Finance
Essential Director
Essential Finance
Essential Internet
Essential Investment
Pocket Asia
Pocket Europe in Figures
Pocket World in Figures
Numbers Guide 5th edn rev3/31 10/19/06 2:49 PM Page iii
NUMBERS GUIDE
The Essentials of Business Numeracy
FIFTH EDITION
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THE ECONOMIST IN ASSOCIATION WITH
PROFILE BOOKS LTD
Published by Profile Books Ltd
3aExmouth House, Pine Street, London ec1r 0jh
www.profilebooks.com
First published by The Economist Books Ltd 1991
Copyright © The Economist Newspaper Ltd, 1991, 1993, 1997, 2001, 2003
Text copyright © Richard Stutely, 1991, 1993, 1997, 2001, 2003
Diagrams copyright © The Economist Newspaper Ltd, 1991, 1993, 1997, 2001, 2003
All rights reserved. Without limiting the rights under copyright reserved above, no
part of this publication may be reproduced, stored in or introduced into a retrieval
system, or transmitted, in any form or by any means (electronic, mechanical,
photocopying, recording or otherwise), without the prior written permission of both
the copyright owner and the publisher of this book.
The greatest care has been taken in compiling this book.
However, no responsibility can be accepted by the publishers or compilers
for the accuracy of the information presented.
Where opinion is expressed it is that of the author and does not necessarily coincide
with the editorial views of The Economist Newspaper.
Typeset by International Typesetters Inc.
[email protected]
Printed in Great Britain by
Creative Print and Design (Wales), Ebbw Vale
A CIP catalogue record for this book is available
from the British Library
ISBN-10 1 86197 515 5
ISBN-13 978 1 86197 515 7
For information on other Economist Books, visit
www.profilebooks.com
www.economist.com
Numbers Guide 5th edn rev3/31 10/19/06 2:49 PM Page v
Contents
List of tables vii
List of figures vii
Introduction 1
1 Key concepts 6
Summary 6
Ways of looking at data 6
Fractions, percentages and proportions 8
Index numbers 14
Notation 17
Probability 21
Counting techniques 27
Encryption 31
2 Finance and investment 33
Summary 33
Interest 33
Annuities 43
Investment analysis 47
Inflation 51
Interest rate problems in disguise 52
Exchange rates 53
3 Descriptive measures for interpretation and analysis 57
Summary 57
Distributions 57
Normal distributions 65
4 Tables and charts 74
Summary 74
Tables 74
Charts 77
5 Forecasting techniques 88
Summary 88
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Time series 89
Trends 94
Seasonal adjustment 98
Cycles 102
Residuals 102
Cause and effect 103
Identifying relationships with regression analysis 104
Forecast monitoring and review 113
6 Sampling and hypothesis testing 116
Summary 116
Estimating statistics and parameters 116
Confidence 121
Other summary measures 124
Non-parametric methods 129
Hypothesis testing 130
7 Incorporating judgments into decisions 137
Summary 137
Uncertainty and risk 137
Decision trees 141
Perfect information 145
The expected value of sample information 147
Making the final decision 151
8 Decision-making in action 157
Summary 157
Game strategy 157
Queueing 161
Stock control 164
Markov chains: what happens next? 166
Project management 170
Simulation 172
9 Linear programming and networking 175
Summary 175
Identifying the optimal solution 175
Traps and tricks 180
Multiple objectives 180
Networks 181
A–Z 185
Index 241
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List of tables
1.1 Mr and Mrs Average’s shopping basket 13
1.2 A base-weighted index of living costs 13
1.3 A current-weighted index of living costs 14
1.4 Index comparisons 15
2.1 Critical compounding 39
2.2 Comparing internal rates of return 48
2.3 Exchange rates and time 54
3.1 Salaries at Backstreet Byproducts 59
3.2 The normal distribution: z scores 68
4.1 Tabular analysis 76
5.1 Calculating a three-month moving average 94
5.2 Exponential smoothing 97
5.3 Analysing seasonality in a short run of data 99
5.4 Full seasonal adjustment 101
5.5 Forecast monitoring and review 114
6.1 Useful z scores 122
7.1 Basic decision table for King Burgers 138
7.2 Three decision techniques for uncertainty 138
7.3 Summary of decisions under uncertainty 140
7.4 Expected payoffs 140
7.5 Expected utilities 144
7.6 Expected payoff with perfect information 146
7.7 Revising probabilities 146
7.8 Summary of King Burgers’ revised probabilities 148
8.1 Corinthian v Regency payoff matrix 158
8.2 The game plan 159
8.3 How long is a queue? 163
8.4 A stockmarket transition matrix 167
8.5 The stockmarket in transition 168
8.6 Probability distribution to random numbers 173
9.1 Zak’s shipping 176
9.2 Corner points from Zak’s graph 178
List of figures
1.1 Number values 9
1.2 The index number “convergence illusion” 15
1.3 Multiple events 25
1.4 Counting techniques 27
1.5 Combinations and permutations 29
2.1 Annuities in action 43
3.1 Summarising a distribution 58
3.2 A normal distribution 65
3.3 Areas under the normal distribution 67
3.4 Non-symmetrical targets 70
3.5 Mr Ford’s expected sales 71
4.1 Anatomy of a graph 77
4.2 Vertical range 78
4.3 Euro against the dollar 78
4.4 A misleading line of enquiry 79
vii
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4.5 More bribes, less money 79
4.6 British labour market 80
4.7a Interest rates 80
4.7b Bouncing back 80
4.8 Commodity prices 81
4.9 Human Development Index 81
4.10 GDP forecasts 82
4.11 Foreign-exchange reserves 82
4.12 Relatives 83
4.13 Living above our means 83
4.14 Dividing the pie 84
4.15 Politics in proportion 85
4.16 Average annual migration, 1995–2000 86
4.17 Out of the frame 86
4.18 Four ways of watching wages 87
5.1 Choosing the main approach 89
5.2 Components of a time series 92
5.3 Moving averages in action 95
5.4 Exponential smoothing 97
5.5 A seasonal pattern around a trend 100
5.6 Identifying a straight line 106
5.7 Sample correlation coefficients 108
5.8 Slow start 108
5.9 Slow finish 109
5.10 A logarithmic transformation 110
5.11 A typical product life cycle 111
5.12 Residuals 113
6.1 The mean ±1.96 standard deviation 120
6.2 Gnomes at a 99% confidence level 132
6.3 Harry’s decision options 133
6.4 Identifying beta 134
7.1 A simple decision tree 141
7.2 Utility curves 142
7.3 The standard gamble 143
7.4 Pessimist King’s utility assessment 144
7.5 A utility curve again 145
7.6 A two-step decision tree 149
7.7 Optimum sample size 151
7.8 Break even analysis and the normal distribution 153
7.9 Marginal analysis and the normal distribution 156
8.1 Inventory costs 164
8.2 Stock replenishment and consumption 165
8.3 Critical path in boat building 170
9.1 Zak’s problem in pictures 177
9.2 Identifying the optimal solution to Zak’s problem 177
9.3 Tricky linear problems 179
9.4 Shortest path 181
9.5 Shortest span 182
9.6 Maximal flow 183
Numbers Guide 5th edn rev3/31 10/19/06 2:49 PM Page 1
Introduction
“Statistical thinking will one day be as necessary a
qualification for efficient citizenship as
the ability to read and write.”
H.G. Wells
This book is about solving problems and making decisions using
numerical methods. Everyone – people in business, social adminis-
trators, bankers – can do their jobs better if equipped with such tools. No
special skills or prior knowledge are required. Numerical methods
amount to little more than applied logic: they all reduce to step-by-step
instructions and can be processed by simple computing devices. Yet
numerical methods are exciting and powerful. They work magic, which
is perhaps why they are shrouded in mystery. This book strips away
that mystery and provides a guided tour through the statistical work-
shop. There are no secrets, no barriers to entry. Anyone can use these
tools. Everyone should.
What are numerical methods?
Numerical methods range from the simple (how to calculate percent-
ages and interest) to the relatively complex (how to evaluate competing
investment opportunities); from the concrete (how to find the shortest
route for deliveries) to the vague (how to deal with possible levels of
sales or market share). The link is quantitative analysis, a scientific
approach.
This does not mean that qualitative factors (intangibles such as per-
sonal opinion, hunch, technological change and environmental aware-
ness) should be ignored. On the contrary, they must be brought into the
decision process, but in a clear, unemotional way. Thus, a major part of
this book is devoted to dealing with risk. After all, this forms a major
part of the business environment. Quantifying risk and incorporating it
into the decision-making process is essential for successful business.
In bringing together quantitative techniques, the book borrows heav-
ily from mathematics and statistics and also from other fields, such as
accounting and economics.
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